Missing second-order nonlinearity in centrosymmetric graphene overshadows its intriguing optical attribute. Here, we report redox-governed charge doping could effectively break the centrosymmetry of bilayer graphene (BLG), enabling a strong second harmonic generation (SHG) with a strength close to that of the well-known monolayer MoS. Verified from control experiments with electrical current annealing and electrically gate-controlled SHG, the required centrosymmetry breaking of the emerging SHG arises from the charge-doping on the bottom layer of BLG by the oxygen/water redox couple. Our results not only reveal that charge doping is an effective way to break the inversion symmetry of BLG despite its strong interlayer coupling but also indicate that SHG spectroscopy is a valid technique to probe molecular doping on two-dimensional materials.